Local modal regression

Figures & data

Figure 1. Plot of negative normal densities.

Table 1. Relative efficiency between the LLMR estimator and the LLR estimator.

Error distribution	Relative efficiency
N(0, 1)	1
	1.1745
	1.6801
t-distribution with df=5	1.1898
t-distribution with df=3	1.7169

Table 2. Relative efficiency between different estimators and the LLH estimator.

Error distribution	n	RE(LLR)	RE(LMED)	RE(LM)	RE(LLMR)
N(0, 1)	50	1	0.6676	0.9235	0.9979
	100	1	0.6757	0.9358	0.9992
	250	1	0.6753	0.9455	0.9997
	500	1	0.6818	0.9488	0.9998
	50	0.6446	0.7314	0.9392	0.9127
	100	0.5828	0.7113	0.9298	0.9210
	250	0.5598	0.7222	0.9375	0.9675
	500	0.5691	0.7246	0.9402	0.9859
t 3	50	0.6948	0.8196	0.9809	0.9514
	100	0.6429	0.8386	0.9611	0.9350
	250	0.5462	0.8470	0.9428	0.9617
	500	0.5743	0.8497	0.9442	0.9747

Figure 2. Plot of fitted regression curves for the Education Expenditure Data. The star point represents the extreme observation from Hawaii. The solid curve represents the LLR fit. The dashed curve represents the LLMR fit.